Base field 4.4.5125.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 7x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[45,15,w^{3} - 5w - 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 8x^{2} + 15x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{2} + 2w + 3]$ | $\phantom{-}1$ |
| 9 | $[9, 3, w^{3} - 3w^{2} - 2w + 9]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{3} + 5w + 5]$ | $-1$ |
| 11 | $[11, 11, w]$ | $-e^{2} - 5e - 2$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}e^{2} + 6e + 4$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{2} + 3e - 5$ |
| 19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-2e^{2} - 9e - 6$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w + 2]$ | $-e^{2} - 5e - 2$ |
| 29 | $[29, 29, w^{3} - 4w^{2} - w + 10]$ | $\phantom{-}2e^{2} + 6e - 10$ |
| 29 | $[29, 29, -w^{3} + 3w^{2} + w - 7]$ | $\phantom{-}e^{2} + 3e - 4$ |
| 41 | $[41, 41, 3w^{2} - 2w - 10]$ | $\phantom{-}e^{2} + 6e + 2$ |
| 49 | $[49, 7, -2w^{2} + 3w + 8]$ | $-3e^{2} - 12e + 2$ |
| 49 | $[49, 7, w^{3} - 2w^{2} - 2w + 5]$ | $\phantom{-}3e^{2} + 12e - 6$ |
| 71 | $[71, 71, -w - 3]$ | $-4e^{2} - 19e - 6$ |
| 71 | $[71, 71, w - 4]$ | $\phantom{-}e^{2} + 2e - 8$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 3w + 3]$ | $\phantom{-}e^{2} + 9e + 6$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $-e^{2} - 5e + 2$ |
| 89 | $[89, 89, w^{3} - 3w^{2} - 3w + 7]$ | $-3e^{2} - 12e - 6$ |
| 89 | $[89, 89, w^{3} - 6w - 2]$ | $\phantom{-}5e^{2} + 20e - 6$ |
| 101 | $[101, 101, 2w^{3} - 5w^{2} - 3w + 9]$ | $\phantom{-}4e^{2} + 21e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w^{2} + 4]$ | $-1$ |
| $9$ | $[9,3,-w^{3} + 5w + 5]$ | $1$ |